Is it still 1966 when they arrive in NY? I've read that the book spans the '60s and '70s; but I've never read the book, so I don't know when they arrive in the US.
Since this production is new, and the twin towers would have to have been digitally added, surely someone would have checked...?
It's clearly later than 1966 because Eamonn and Cathy have grown up, so it's well into the 70's when Eamonn and his dad arrive in NYC. Construction on the North Tower finished on December 23, 1970, and construction on the South Tower finished later on July 19, 1971.
''All those moments will be lost in time, like tears in rain .... Time to die''.
Episode 4 clearly states "Four years later, June 1971" at the beginning - implying that all previous episodes, including the Dochertys' arrival to NYC, took place in 1966/1967.